EPA-650/2-74-110
OCTOBER 1974
Environmental Protection Technology Series
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EPA-650/2-74-110
MATHEMATICAL SIMULATION
OF AN ADSORBER
FOR POLLUTANT REMOVAL
by
L. T. Fan
Kansas State University
Manhattan, Kansas 66506
Grant No. R-800316
ROAP No. 21AXM-061a
Program Element No. 1AB015
EPA Project Officer: Belur N. Murthy
Control Systems Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D .C . 20460
October 1974
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
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I'INAI. KKI'OKT
MATIIKMATICAI, SIMULATION OK AN ADSOKKKK
R)K I'OI.UJTANT KKMOVAJ.
by
L. T. Fan
A Research Project Conducted
at
Department of Chemical Engineering
Kansas State University
Manhattan, Kansas 66506
Juno L, ]972 Ln M.iy '31 , J973
AcknowlcdgomonL
This study is supported by the Environmental Protection Agenc-y (Project No.
R-800316)
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MATHMATICAL SIMULATION OF AN ADSORBER
FOR POLLUTANT REMOVAL
ABSTRACT
An extensive survey of the literature on design and operation of fixed
bed adsorbers is given and available mathematical models for adsorption pro-
cesses are summarized. Results of simulation of an adiabatic adsorber are
presented, based on an axial dispersion modeJ with external mass transfer
rate control and Langmuir type Isotherm. Numerical values of the dynamu.
adsorbate concentrations and temperature at various positions of the bed
are obtained by means of the Crank-Nicolson implicit method. The effects
of various parameters are investigated thoroughly to give an insight into the
operating characteristics of such an adsorber.
Two schemes are proposed for operating a single fixed bed to remove
the pollutant continuously. One uses fresh air for desorption and the other
uses exhaust gas for desorption. Generally, the pollutant Is adsorbed jt
a temperature lower than it is desorbed, and the desorbed pollutant is then
burned and disposed. Effects of several parameters on the adsorber per-
formance are studied through computer simulation. The results of this study
can serve as a guideline in designing a single bed adsorber system.
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I I
CONTENTS
Pjg
1. INTRODUCTION 1
2. LITERATURE SURVEY AND MATHEMATJCAL MODELING 3
3. MODELING AND SIMULATION OF AN AD1ABATIC ADSORBER PKRKORMANCK 21
4. GASEOUS POLLUTANT REMOVAL BY A SINGLE BED CYCLIC ADSORBER WITH
SYNCHRONOUS THERMAL CONTACT 53
5. CONCLUSIONS AND RECOMMENDATIONS 89
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1. INTRODUCTION
The adsorption process has been employed mostly in the separation of
fluids and solvent recovery. Increasingly the adsorption process is being
employed for pollutant removal from air. In the first section of this
report, a comprehensive survey of the literature on design and operational
aspects of processes for adsorbing gaseous pollutants is given. Mathema-
tical models of these processes are also summarized. In the second section
of this report, mathematical models for the adiabatic adsorption processes
in a fixed bed of adsorbent are presented. The models take into account
axial dispersion of the pollutant and are based on the mechanisms of
external mass transfer rate control and a Langmuir type isotherm. The
transient solution is presented for the dynamic adsorbate concentrations
and temperature at various positions of the bed. The solution was
obtained by solving numerically the governing equations using the Crank-
Nicolson implicit method. Results of the studies on the effects of various
parameters are also presented. The third section of this report, describes
a single fixed bed pollutant adsorber operated cyclically by synchronizing
the change in the direction of the gaseous flow with the change in
temperature. Two operational schemes are presented for such a system.
Effects of several parameters on the adsorber performance are discussed.
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2. LITERATURE SURVEY AND MATHEMATICAL MODELING
A packed bed adsorber can be used for controlling gaseous pollutants
(Hirschler and Amon, 1947; Mair et al., 1947; Lorentz, 1950; Turk and
Bownes, 1951; Turk, 1968; Lippmaa and Luiga, 1970; Mattia, 1970; Turk,
1970; Turk et al., 1972). This report presents a comprehensive survey
of the literature on design and operational aspects of gas adsorbers
which are employed for controlling obnoxious substances emitted from
stationary sources such as restaurants, auto repair or paint shops,
gasoline storage and transfer areas, dry cleaning shops, industrial
factories, and process plants. Although the pollutant emission from
any of such sources may often be negligible in quantity, the pollutants
(mostly aromatic hydrocarbons) have objectionable properties such as
odor or toxicity (Patty, 1942; Hayashi and Hayashi, 1969). In addition,
there is a large number of such sources and, therefore, the overall
contribution of these sources to air pollution is significant. Available
and plausible "operational" mathematical models of the adsorbers are
also summarized in this report.
An adsorption unit which consists of two fixed bed columns of
adsorbent is considered in this section. In the cycle of
operation, one of the columns is always in the regeneration mode and
the other is in the adsorption mode. Activated carbon is most frequently
employed as the adsorbent since it is commercially available in quantity
and adsorbs essentially all types of organic gases and vapors regardless
of variation in concentration and humidity. The recently invented doped
active carbons (Inagaki, 1970) and sieving active carbons (Kawazoe et al.,
1971; Takeuchi et al., 1972) can also be employed.
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A mathematical model for a fixed adsorption bed should take into
account, at least, the dynamic changes of the adsorbate concentrations
i
in both the gaseous and solid phases at various positions in the bed.
Some published papers on modeling the adsorption processes in fixed
beds (Vermeulen, 1958; Masamune and Smith, 1964; Carter, 1966; Meyer
and Weber, 1967; Schneider and Smith, 1968; Lee and Weber, 1969a,
1969b; Chu and Tsang, 1971; Gariepy and Zwiebel, 1971; Thomas and
Lombardi, 1971; Carter and Husain, 1972; Cooney and Shieh, 1972;
Cooney and Strusi, 1972; Gupta and Greenkorn, 1972; Tada et al.,
1972b) are available. Modeling of the concentration dynamics can
usually be accomplished either by taking a mass balance (for an isothermal
process) or by taking mass and energy balances (for a nonisothermal
process) over a control volume of the bed. Interphase mass or heat
transport is often considered to be the rate controlling mechanism
(Geser and Canjar, 1962; Carter, 1966; Meyer and Weber, 1967; Hiraoka
et al., 1968; Rimpel et al., 1968; Schneider and Smith, 1968; Lee and
Weber, 1969a, 1969b; Masamune and Smith, 1969; Gariepy and Zwiebel,
1971; Thomas and Lombardi, 1971; Carter and Husain, 1972; Cooney and
Shieh, 1972; Cooney and Strusi, 1972; Ikeda et al., 1972).
Since the rate of interphase mass transfer depends on the degree
of saturation of adsorbate on adsorbent, knowledge of the equilibrium
state is required in modeling it. Mathematical models for the various
types of equilibrium states have been delineated (Brunauer, 1943;
Young and Crowell, 1962). Experimental equilibrium data, specifically
those for the adsorption of gaseous hydrocarbons on activated carbon,
and the various adsorption equilibrium models to represent such data
are available (Brunauer et al., 1938; Lewis et al., 1950; Kapfer et al.,
1956; Geser and Canjar, 1962; Grant et al., 1962; Cook and Basmadjian,
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5
1964; Grant and Manes, 1964; Meyer and Weber, 1967; Lee and Weber, 1969b;
Clapham et al., 1970; McCarthy, 1971; Thomas and Lombard!, 1971).
A mathematical model for regeneration of deactivated adsorbent is
also necessary in developing the optimum design and operating procedure
of an adsorption system since the system includes both adsorption and
regeneration steps in its cyclic operation. The regeneration of deacti-
vated adsorbent is usually carried out by raising the temperature of
the adsorbent. For example, the regeneration of deactivated carbon is
accomplished by passing saturated steam at low pressure countercurrently
through the carbon bed. Although the regeneration process is often referred
to as a reverse process of adsorption, experimental data as well as theoretical
analysis to support this hypothesis are meager. It has been reported,
however, that there is no indication of the existence of a hysteresis
phenomenon in adsorption and desorption (Lewis et al., 1950).
To predict the adsorbate concentration change in the bed with respect
to time, the mass balance or the mass and energy balances given in the
form of differential equations must be solved either analytically or
numerically. For the case of simple linear differential equation the
analytical solution can be obtained (Bohart and Adams, 1920; Thomas,
1944; Hiester and Vermeulen, 1952; Masamune and Smith, 1964; Gupta
and Greenkorn, 1972). The governing equations are usually nonlinear
differential equations. Furthermore, if the adsorption unit is operated
nonisothermally, the governing equations are two coupled nonlinear
partial differential equations. For these cases, the analytical solutions
may not be available; however, various numerical methods can be used
for the solution (Rosen, 1954; Lapidus, 1962; Liu and Amundson, 1962;
Smith, 1965; Rosenbrock and Storey, 1966; Villadsen and Stewart, 1967;
Finlayson, 1969; Forsythe and Wasow, 1969; Liu, 1969; Stewart, 1969;
Chu and Tsang, 1971; Tada et al., 1972a).
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2.1. MODELS OF ADSORPTION STEP
The mathematical expression for the rate of adsorption can be
derived based on the known and/or postulated transport mechanism of
the adsorbate. Such mechanism is often considered to consist of the
following possible sequence of steps: (a) transport of adsorbate
from the bulk of the fluid to the external surface of the adsorbent,
(b) transport from the external surface into the interior surface
of the adsorbent, and (c) adsorption on the adsorbent surface. Although
each step offers' resistance to adsorbate transport, a single rate
controlling step is often considered to provide the major portion of
the overall resistance. There can be, therefore, three types of rate
controlling models, each of them giving a different form of the rate
expression for adsorption.
(a) External mass transfer controlling
Ra = k po a(c - c*) (1)
a eg
(b) Intraparticle diffusion controlling
Ra ' Di a pg
3c
where (T — ) is determined by solving the differential equation
3r r=rQ
32c. - 3c 9c
<3>
with initial and boundary conditions
when t = 0, c. = 0
at r = 0, - = 0
(A)
-------
at r = rQ, c± = c(z, t)
(c) Surface adsorption controlling
R = k Sc p (1 - -S-) - k. S -3- (5)
a a g q°" d q°°
Notations employed in these equations are defined as follows:
R = overall rate of adsorption per unit volume of bed,
a 3
g/sec-cm
k = external mass transfer coefficient based on external
e
surface of particle and concentration driving force,
cm/sec
a = available external surface area per unit volume of
U J 2/ 3
bed, cm /cm
c = mass fraction of adsorbate in the bulk fluid, g of
adsorbate/g of adsorbate free gas
c. = mass fraction of adsorbate of the fluid in the particle,
g of adsorbate/g of adsorbate free gas
H = gas phase hold-up, i.e., mass of gas per unit volume
8 3
of bed, g of gas/cm of bed
H = solid phase hold-up, i.e., mass of adsorbent per unit
S 3
volume of bed, g of adsorbent/cm of bed
2
D. = effective intraparticle diffusivity, cm /sec
c* = equilibrium composition, g of adsorbate/g of adsorbate
free gas
r = radial distance from center of spherical particle, cm
r_ = radius of spherLcdl particle, cm
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3
p = density of gas, g/cm
o
t = time, sec
qeo = maximum amount of adsorbate which can be adsorbed per
unit mass of adsorbent, g of adsorbate/g of adsorbent
q = amount of adsorbate adsorbed per unit mass of adsorbent,
g of adsorbate/g of adsorbent
z = axial distance from entrance of bed, cm
k = adsorption rate constant per unit surface area of pores,
cm/sec
2 3
S = pore surface area per unit volume of bed, cm /cm
k, = desorption rate constant per unit surface area of pores,
g/sec-cm
Since the adsorption rate depends on the degree of saturation of
adsorbate on adsorbent, a mathematical model for the equilibrium state
is necessary to express the rate equation explicitly. A variety of
mathematical expressions based on various adsorption theories such
as Langmuir's monolayer theory (Langmuir, 1918, 1932; Brunauer, 1943;
Suits, 1961; Young and Crowell, 1962), Freundlich's equation (Freundlich,
1922; Brunauer, 1943), Polanyi's potential theory (Brunauer, 1943;
Young and Crowell, 1962), the capillary condensation theory (McGavack
and Patrick, 1920; Brunauer, 1943), and the BET equation (Brunauer
et al., 1938; Brunauer et al., 1940; Brunauer, 1943; Young and Crowell,
1962) are available. For example, the BLT equation based on the finite
multilayer theory can be written in terms of vapor pressure as
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1--B-
p
o
i i -L iw_P_\n _i_ / p xn+l
1 - (n + 1) (-*—) + n(-t-)
1 + (b, - 1) (-P-) -
0
, (AH - AH )/RT ,,.
b = ev a c (7)
where
p = vapor pressure, mm Hg or psi
pn = saturated vapor pressure at temperature T, mm Hg or psi
n = number of layers
AH = heat of adsorption, cal/g-mole
a
AH = heat of condensation, cal/g-mole
R = gas constant, cal/g-mole-°K
T = temperature, °K
The BET equation, equation (6), becomes identical to the expression of
Langmuir's monolayer theory (Type I isotherm), if n = 1. If n > 1,
either Type II or Type III isotherm is obtained, depending on the value
of constant b...
Regeneration Rate Equation: The rate expression for the regeneration
step should be similar to the rate equation for the adsorption step
with the exception that directions of adsorbate transport in the two
steps are opposite. The identical equilibrium equation can also be
employed since there is no indication of the existence of a hysteresis
phenomenon associated with the adsorption-desorption cycle (Lewis
et al., 1950).
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10
2.2. FLOW MODELS
It Is very difficult to represent mathematically the precise flow
behavior of the fluid as it passes through the adsorption bed. However,
based on some simplifying assumptions, the flow pattern in the bed may
be approximated by different flow models, for example, the back-mix
(completely mixed) flow model, plug flow model, and nonideal flow models
such as the dispersion model, the compartment model, and the combined
or mixed model (Levenspiel, 1962; Wen and Fan, 1974). The back-mix
model (Levenspiel, 1962; Denbigh, 1966; Wen and Fan, 1974) assumes
that the adsorbate concentration of the fluid is uniform throughout
the bed. The governing equations for the model may be written as
" ' <<0 - c> + Ra
with initial conditions
c = q = 0 when t = 0 (9)
where T is the mean residence time based on the mass flow rate and
cn is the inlet adsorbate concentration. This model is an oversimplified
model for the flow through a fixed bed. It may serve, however, as a
very rough approximation of the flow under certain circumstances where
the effect of mixing is more significant than that of the overall
convective motion in the bed. It may also serve as one of the two
limiting or ideal cases which bound the actual flow behavior.
If the overall convective motion affects predominantly the movement
of adsorbate, the plug flow model (Levenspiel, 1962; Denbigh, 1966;
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11
Wen and Fan, 1974) approximates the flow better. The plug flow model
(also called the piston flow model) assumes that no mixing of adsorbate
is induced among elements of the fluid at different positions along
the direction of flow; that is to say, the.fluid is assumed to move
through the adsorption bed like a plug. The governing equations for
the model may be written as
H l£ = _ G l£ _ R
g 3t 3z a
"s • "a <">
with initial and boundary conditions
when t=0, c=q=0 (12)
at z = 0, c = CQ (13)
2
where G is the superficial mass flow rate of fluid (g of gas/sec-cm ).
In practice, this model is more frequently used than any other in
modeling a packed bed (Masamune and Smith, 1964; Carter, 1966; Meyer
and Weber, 1967; Rimpel et al., 1968; Lee and Weber, 1969a, 1969b;
Gariepy and Zwiebel, 1971; Thomas and Lombard!, 1971; Carter and Husain,
1972; Cooney and Shieh, 1972). This model also serves as a limiting
or an ideal case which bounds the actual flow.
The actual flow pattern is neither a back-mix flow nor a plug
flow. Therefore, the use of one of many available nonideal flow models
that take into account the effect of axial and/or radial dispersion is
desirable. If the (axial) dispersion model (Levenspiel, 1962; Denbigh,
1966; Wen and Fan, 1974) is employed, the governing equations are
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12
H = 4, p E. - G - R (14)
g at g 1 . i dz a
•. H
with initial and boundary conditions
when t = 0, c=q=0 (16)
at z = °- G(CW = CC0 + * pg VflW
(17)
at z = L, |J - 0 (18)
where E. is the axial dispersion coefficient and 41 is the void fraction
of the bed. Here, the second boundary condition may not be rigorous
since the condition at the exit of the finite bed is changing with
respect to time for an unsteady state process. Since the time constant
of concentration change at the exit is much larger than the length of
the operating time, it may not be erroneous to use such a boundary
condition. Some published papers employing this flow model are
available (Schneider and Smith, 1968; Chu and Tsang, 1969; Cooney
and Strusi, 1972; Gupta and Greenkorn, 1972; Ikeda et al., 1972).
Other nonideal flow models which are often employed to approximate
the actual flow pattern through a fixed bed are the compartment model
and the combined model (Levenspiel, 1962; Denbigh, 1966; Wen and Fan,
1974)i The compartment model (also called the cell model) (Deans and
Lapidus, 1960; Levenspiel, 1962; Wen and Fan, 1974) is based on a
two-dimensional network of completely mixed tanks. If the radial
concentration gradient in the fixed bed is negligibly small, the
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13
two-dimensional network becomes a one-dimensional completely mixed
tanks-in-series (with and without backflow). The governing equations
for the model are derived from the input-output-accumulation analysis
for all the cells. For the case of negligible radial concentration
gradient, the compartment model is nearly equivalent to the axial
dispersion model.
The combined model (also called the mixed model) assumes that
the actual flow pattern is approximated by combinations of various
ideal and nonideal flow models in parallel or in series or in mixed
fashion. In addition, the model takes into account the effects of
bypass flow, recycle flow and cross flow as well as dead space in
the system. The governing equations for the model are obtained from
the individual governing equations for the component systems and
from the mode of combinations of the component systems with the
bypass, recycle, and cross flows.
Isothermal and Nonisothermal Processes: Isothermal adsorption precludes
heat effects; therefore, analysis can be based only on the material
balance on adsorbate and the equilibrium relationship between adsorbate
in the fluid and that in the adsorbent. The application is restricted
to systems that have low inlet adsorbate concentration and high fluid
velocity. This is also applicable to systems that have small heat of
adsorption.
In practice, it is difficult to maintain strictly isothermal con-
ditions since the adsorption process can be accompanied by considerable
heat generation (Brunauer, 1943; Young and Crowell, 1962). The heat
released in the adsorption process raises the temperature of the bed,
and the rise in temperature decreases the adsorption rate. Therefore,
analysis should include changes in energy as well as in the adsorbate
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14
concentrations in both the body of the fluid and the adsorbent. For
example, for the flow pattern represented by the dispersion model,
the governing equations expressed in equations (14) through (18)
should be accompanied by the energy balances
3T 32T 3T
Hg Cg It = * E2 - Gcg 3 - h a(Tg - V
, 3T 92T
Hs Cs aT ' (1 - *)E3 T + h a(Tg - Ts) + VAH) (20)
The initial and boundary conditions are
when t = 0, T = Tg = TQ (21)
3T
Gcg(yz=o+ ' Gcg To + * VaW (22)
3T f
at z = 0, -LSQ (22a)
3T 3T
at Z = L« = = ° (23)
where
E2 = thermal conductivity of gas in flow through the bed,
cal/sec-°K-cm
h •* heat transfer coefficient between gas and adsorbent,
cal/°K-cm -sec
3
p = density of gas, g/cm
O
c = specific heat of gas, cal/°K-g
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15
T = gas temperature, °K
g
T = solid temperature, °K
s
E, = thermal conductivity of solid, cal/sec-°K-cm
3
p = density of solid adsorbent, g/cm
c = specific heat of solid adsorbent, cal/°K-g
S
AH = average heat of adsorption, cal/g
TQ = temperature at the inlet of the bed, °K
Recent noteworthy works on adsorption that have not been
discussed so far are those by Ikeda et al. (1972), Tada et al.
(1972a), Tada et al. (1972b).
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16
Bohart, G. S. and E. Q. Adams, "Some Aspects of the Behavior of
Charcoal with Respect to Chlorine," Am. Chem. Soc. J., 42, 523-544
(1920).
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Multimolecular Layers," J. Am. Chem. Soc., 60, 309-319 (1938).
Brunauer, S., L. S. Deming, W. E. Deming, and E. Teller, "On a Theory
of the Van der Waals Adsorption of Gases," J. Am. Chem. Soc., 62,
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Brunauer, S., "The Adsorption of Gases and Vapors, Volume I, Physical
Adsorption," Princeton University Press, Princeton, N.J. (1943).
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Carter, J. W. and H. Husain, "Adsorption of Carbon Dioxide in Fixed
Beds of Molecular Sieves," Trans. Instn. Chem. Engrs., 50, 69-75
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Chu, C. and L. C. Tsang, "Behavior of a Chromatographic Reactor,"
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Cook, W. H. and D. Basmadjian, "Correlation of Adsorption Equilibria
of Pure Gases on Activated Carbon," Can. J. Chem. Eng., 42, 146-151
(1964).
Cooney, D. 0. and D. Shieh, "Fixed Bed Sorption with Recycle," AIChE
Journal, 18, 245-247 (1972).
Cooney, D. 0. and F. P. Strusi, "Analytical Description of Fixed-Bed
Sorption of Two Langmulr Solutes Under Nonequilibrium Conditions,"
Ind. Eng. Chem. Fundam., JL1, 123-126 (1972).
Deans, H. A. and L. Lapidus, "A Computational Model for Predicting
and Correlating the Behavior of Fixed-Bed Reactors," AIChE Journal,
6., 656-663 (1960).
Denbigh, K., "Chemical Reactor Theory," Cambridge University Press,
Cambridge, Mass. (1966).
Finlayson, B. A., "Applications of the Method of Weighted Residuals
and Variatlonal Methods," British Chem. Eng., 1.4, 53-57, 179-182
(1969).
Forsythe, G. E. and W. R. Wasow, "Finite-Difference Methods for Partial
Differential Equations," AIChE Journal, J^, 334-338 (1969).
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17
Freundlich, H., "Colloid and Capillary Chemistry," E. P. Dutton and
Co. Inc., New York (1922).
Gariepy, R. L. and I. Zwiebel, "Adsorption of Binary Mixtures in Fixed
Beds," a paper presented at the 68th National Meeting of the AIChE,
Houston, Texas, Feb. 28 - March 4 (1971).
Geser, J. J. and L. N. Canjar, "Adsorption of Methan and Hydrogen
on Packed Beds of Activated Carbon," AIChE Journal, 8, 494-497
(1962).
Grant, R. J., M. Manes, and S. B. Smith, "Adsorption of Normal Paraffins
and Sulfur Compounds on Activated Carbon," AIChE Journal, J3, 403-406
(1962).
Grant, R. J. and M. Manes, "Correlation of Some Gas Adsorption Data
Extending to Low Pressures and Supercritical Temperatures," Ind. Eng.
Chem. Fundamentals, JJ, 221-224 (1964).
Gupta, S. P. and R. A. Greenkorn, "Dispersion During Flow in Porous
Media with Adsorption," a paper presented at the 72nd National Meeting
of the AIChE, St. Louis, Mo., May 21-24 (1972).
Hayashi, M. and S. Hayashi, "Nuisance Caused by Odor," Proceedings
of The Osaka Prefectural Institute of Public Health, Edition of
Industrial Health No. 7, September (1969).
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Exchange and Adsorption Columns," Chem. Eng. Prog., 48, 505-516
(1952).
Hiraoka, M., G. Matsuno, and T. Hanakawa, "A Consideration on the
Mechanism of S02 Gas Adsorption on Activated Carbon," Air Conditioning
and Sanitary Eng. (Japan), 42^ 503-509 (1968).
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of high-purity saturated hydrocarbons," Ind. Eng. Chem., 39. 1585-1596
(1947).
Ikeda, K., 0. Kanemitsu and K. Shimomura, "Fixed Bed Gas Adsorption
under High Pressure," a paper presented at the 37th annual meeting
of the Society of Chemical Engineers, Japan, Nagoya, Japan, April
(1972).
Inagaki, K., "SOn Removal from Exhaust Gases by Adsorbents Catalyzed
with Metallic Oxides," Aichi-Ken Kogyo Shidosho Report, Nogoya, Japan
(1970).
Kapfer, W. H., M. Malow, J. Happel, and C. J. Marcel, "Fraction of
Gas Mixtures in a Moving-bed Adsorber," AIChE Journal, JJ, 456-467
(1956).
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18
Kawazoe, K., V. A. Astakhov, T. Kawai, and Y. Eguchi, "Adsorption
Equilibrium on Molecular-sieving Carbon," Kagaku Kogaku (Chemical
Engineering, Japan), j)5, 1006-1011 (1971).
Langmuir, I., "The Adsorption of Gases on Plane Surfaces of Glass,
Mica and Platinum," J. Am. Chem. Soc., 40, 1361-1403 (1918).
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J. Am. Chem. Soc., 54, 2798-2832 (1932).
Lapidus, L., "Digital Computation for Chemical Engineering," McGraw-Hill
Co., New York (1962).
Lee, R. G. and T. W. Weber, "Isothermal Adsorption in Fixed Beds,"
Can. J. Chem. Eng., 47_(1), 54-59 (1969a).
Lee, R. G. and T. W. Weber, "Interpretation of Methane Adsorption
on Activated Carbon by Nonisothermal and Isothermal Calculations,"
Can. J. Chem. Eng., 47(1), 60-65 (1969b).
Levenspiel, 0., "Chemical Reaction Engineering," John Wiley & Sons,
New York (1962).
Lewis, W. K., E. R. Filliland, B. Chertow, and W. P. Cadogen, "Pure
Gas Isotherms," Ind. Eng. Chem., 4£, 1326-1332 (1950).
Lippmaa, E. T. and P. 0. Luiga, "Concentration of Organic Air Contaminants
by Sorbents," a paper presented at the 2nd International Clean Air
Congress, Washington, D. C., Dec. 6-11 (1970).
Liu, S. L. and N. R. Amundson, "Stability of Adiabatic Packed Bed
Reactors — An Elementary Treatment," Ind. Eng. Chem. Fundamentals,
1, 200-208 (1962).
Liu, S. L., "Stable Explicit Difference Approximations to Parabolic
Partial Differential Equations," AIChE Journal, ^5, 334-338 (1969).
Lorentz, F., "Waste Disposal," Chem. Eng. Prog., 46J8) , 377-379 (1950).
Mair, B. J., A. L. Gaboriault, and F. D. Rossini, "Assembly and
Testing of 52-Foot Laboratory Adsorption Column — Separation of
hydrocarbons by adsorption," Ind. Eng. Chem., 39, 1072-1081 (1947).
Masamune, S. and J. M. Smith, "Adsorption Rate Studies — Significance
of Pore Diffusion," AIChE Journal, 10, 246-252 (1964).
Mattia, M. M., "Process for Solvent Pollution Control," Chem. Eng.
Prog., 66(12), 74-79 (1970).
McCarthy, W. C., "Adsorption of Light Hydrocarbons from Nitrogen with
Activated Carbon," Ind. Eng. Chem. Process Des. Develop., 10, 13-18
(1971).
-------
McGavack, J., Jr. and W. A. Patrick, "The Adsorption of Sulfur Dioxide
by the Gel of Silicic Acid," J. Am. Chem. Soc., ^2, 946-978 (1920).
Meyer, 0. A. and T. W. Weber, "Nonisothermal Adsorption in Fixed
Beds," AIChE Journal, JL3, 457-465 (1967).
Patty, F. A., editor, "Industrial Hygiene and Toxicology, Vol. II,"
Interscience Publishers, Inc., New York (1942).
Rimpel, A. E., Jr., D. T. Camp, J. A. Kostecki, and L. N. Canjar,
"Kinetics of Physical Adsorption of Propane from Helium on Fixed
Beds of Activated Alumina," AIChE Journal, JL4, 19-24 (1968).
Rosen, J. B., "General Numerical Solution for Solid Diffusion in Fixed
Beds," Ind. Eng. Chem., 46, 1590-1594 (1954).
Rosenbrock, H. H. and C. Storey, "Computational Techniques for Chemical
Engineers," Pergamon Press, New York (1966).
Schneider, P. and J. M. Smith, "Adsorption Rate Constants from
Chromatography," AIChE Journal, 14, 762-771 (1968).
Smith, G. D., "Numerical Solution of Partial Differential Equations,"
Oxford University Press, Oxford (1965).
Stewart, W. E., "Solution of Transport Problems by Collocation Methods,1
AIChE Continuous Education Series, No. 4, pp. 114-135 (1969).
Suits, C. G., editor, "The Collected Works of Irving Langmuir, Vol. 9,
Surface Phenomena," Pergamon Press, New York (1961).
Tada, K., S. Shikagawa, and I. Nakamori, "Measurement of Adsorption
Characteristics by Gas Chromatographic Method, (I)," a paper presented
at the 37th annual meeting of the Society of Chemical Engineers, Japan,
Nagoya, Japan, April (1972a).
Tada, K., S. Shikagawa, and I. Nakamori, "Measurement of Adsorption
Characteristics by Gas Chromatographic Method, (II)," a paper presented
at the 37th annual meeting of the Society of Chemical Engineers,
Japan, Nagoya, Japan, April (1972b).
Takeuchi, T., E. Furutani, and Y. Eguchi, "Liquid Phase Adsorption
Equilibrium on Molecular-sieving Carbon," a paper presented at the
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Nagoya, Japan, April (1972).
Thomas, H. C., "Heterogeneous Ion Exchange in a Flowing System," Am.
Chem. Soc. J., 66, 1664-1666 (1944).
Thomas, W. J. and J. L. Lombardi, "Binary Adsorption of Benzene-Toluene
Mixtures," Trans. Instn. Chem. Engrs., 49, 240-250 (1971).
-------
20
Turk, A. and K. A. Bownes, "Adsorption Can Control Odors," Chem. Eng.,
58(5), 156-158 (1951).
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Butterworth, London (1962).
-------
21
3. MODELING AND SIMULATION OF AN ADLABAT1C ADSOKBF.K I'KKKORMANCK
A packed bed adsorption unit appears to be one of the most practical
devices for controlling gaseous pollutants since it has a relatively
simple structure compared to other possible control devices, and therefore,
can be coupled without much difficulty with various moving and stationary
sources. The mathematical model for a fixed bed adsorption process
generally takes into account the dynamic changes of adsorbate concentra-
tions in both gaseous and solid phases at various positions of the bed.
Modeling of the concentration dynamics can usually be accomplished either
by taking a mass balance (for an isothermal process) or by taking mass
and energy balances (for a nonisothermal process) over a control volume
of the bed.
In the modeling of adsorption processes in fixed beds, external
mass transfer, intraparticle diffusion,or surface adsorption, or a com-
bination of these processes is usually considered to be rate controlling.
The external mass tranfer control model is applicable for cases where the
adsorbent particles are relatively small. The intraparticle diffusion
control model is often used for relatively large adsorbent particles.
The significance of this adsorbate transport step has been verified by
Masamune and Smith , and Rimple, et al. . The surface adsorption
control model is valid only when relatively small resistances are imposed
by the external mass transfer and intraparticle diffusion steps. A com-
bined rate control model of external mass transfer and intraparticle
diffusion has also been used
Since the rate of adsorption depends on the degree of saturation
of adsorbate on adsorbent, knowledge of the equilibrium phenomenon is
-------
22
required in modeling the adsorber performance. Models for various
(3 4)
types of equilibrium states have been extensively delineated .
While a linear equilibrium equation is often used because of its simpli-
city, many of the available equilibrium models give rise to nonlinear
equations; among them are the Langmuir's monolayer theory, Polanyi's
potential theory, capillary condensation theory, Freunlich's model, and
BET model,
The flow pattern of the gas in a fixed bed adsorber also affects
significantly its performance. Although the flow pattern in the fixed
bed adsorber is very difficult to be accurately described mathematically,
it can be approximated by various models; for example, the back-mix
(completely mix) flow model, the plug flow model, and nonideal flow
models such as the dispersion model, the compartment model, and the
combined or mixed model ' , Among these, the plug flow and axial dis-
persion models are the two most frequently employed. The plug flow
model is valid if the adsorber bed is relatively deep and the movement
of the adsorbate is predominated by the convective motion. The model
has been extensively used in modeling both the isothermal ' and
nonisothermal adsorption processes in fixed beds.
The actual flow pattern of a gas through a fixed adsorption bed can
deviate appreciably from that represented by the plug flow. Axial
dispersion of the adsorbate can be caused by the turbulence, influence
of the velocity profile, molecular diffusion, and convective mixing
due to temperature differences. Therefore, the dispersion model is more
realistic than the plug flow model to simulate the flow through a fixed
bed, especially for a shallow bed, However, the application of this
model has been limited thus far to the isothermal case for adsorption
-------
23
processes although it has been extensively employed to simulate
(19-21)
nonlsothermal or adiabatic processes for packed bed catalytic reactions
In this study, the adiabatic adsorption process taking place in
a fixed bed of adsorbent is mathematically modeled and numerically
simulated, The flow of the gas phase in the bed is modeled bv the axial
dispersion model. The mass and heat transfers between the gas and
solid phases are assumed to be external transfer rate controlling while
the equilibrium istherm between the two phases is assumpd to he that of the
Langimiir type. Computer simulation is used to examine the effects of various
design parameters such as the Peclet number, external mass and heat transfer
coefficients, and the adsorbent capacity on the dynamic changes in the
adsorbate concentration and temperature in both gaseous and solid phases
of the bed,
3.1. MODEL EQUATIONS AND NUMERICAL SOLUTIONS
The assumptions made in deriving the model equations for the packed
adsorber under consideration are that
(a) An adsorption process inking place in a fixed bed is adiabatic,
(b) Parameters such as heat and mass transfer coefficients, porosity
of bed, adsorbent density, specific surface area, specific heats
of gas and adsorbent, heat conductivity of adsorbent do not change
with operating conditions, and
(c) No dispersion of the gaseous components occurs in the entrance
and exit sections adjacent to the bed.
Mass and heat balances over a control volume of the bed lead to the
following partial differential equations.
-------
u
n
_ _.
- — • vp Ci. ^ » v« _ •• i\
g 3t Hg 1 3 2 9z a
0)
H
3T
H c -T-4
g g 3t
3T
V.1F
32T
3T
32T
02
ha(T
- Ta>
(2)
(3)
The initial and boundary conditions are:
when t = 0
c = 0
q = 0
T = T_
g 0
T = T.
a 0
(5)
(6)
(7)
(8)
at z =0
G (c)
. = Cc- + *p I
z=0+ f 8
0 C.(V
z=0
. Gc Trt
,+ 8 0
,3c,
z=0
3T
2=0
(10)
3T
£
3z
= 0
(ID
at z = L
= 0
(12)
-------
25
3T
0 (13)
3T
TT
The adsorption rate, R , for the external mass transfer control mechanism
ct
can be written as
R = k a p (c - c*) (15)
a e g
where c* is the gas phase equilibrium concentration which can be expressed
by a Langmuir type isotherm
be*
where
A2
Aj^ exp(— )
b= - — - (17)
T1
a
Let
Y =t
T (18)
u = -
To
V . --
To
-------
26
Pe
t G
L H
g
GL
m
Pe, =
GL
*p
8g
K
k ap L
e g
G
haL
Gc
g
K =
GLHS
H c.
H q
s m
H c
= fi 8.
H c
s s
Cs Hs T0
Then equations (1) through (16) can be transformed into
3X 13 3X .v *
37 - pT TI ' ax ' Ke (x " x
m dA
(19)
(20)
-------
27
Pe. 2 9X
h 3X
(21)
81
K —• + BH(U - V) + YK (X - X*)
3X2
(22)
BX
1 + BX
(23)
The corresponding initial and boundary conditions are:
when T =
X =
Y =
U =
V =
at * =
(X)
(U)
0
0
0
1
1
0
+
+ Pe ^3X'
m
•N.
+ ?e^ W
X=0
(24)
(25)
(26)
(27)
(28)
-= 0
ax °
(30)
at X = 1
3X
(31)
- 0
~ °
(32)
3X
(33)
-------
28
where
i
A2
A. exp(-z-)
B = -± j-^- (34)
(V)2
If the mass dispersion coefficient, E , is assumed to he equal to rhe tlu-rnvil
i
dispersion coefficient, E (or E /p c ), then
Pe = Pe, = Pe (35)
m n
It would be very difficult, if not impossible, to obtain analytical solutions
for the simultaneous partial differential equations, equations (19) through
(23), subject to the initial and boundary conditions, equations (24) to (33).
Computer-aided .numerical methods can be employed for solution. These methods
include the finite difference method, method of characteristics, and collo-
cation method, Among these, the implicit finite difference method, specifically
the Crank-Nicolson method, is employed in this study. The method involves
less stringent stability and convergence restrictions than the explicit
finite difference method and requires less computing time than the method of
characteristics. In addition, this method is known to be particularly power-
ful for the parabolic partial differential equations encountered in this study
In employing the Crank-Nicolson method, each partial differential equation
is rewritten as a set of simultaneous algebraic equations. Since a detailed
(22 23)
description of the method is available elsewhere ' , the derivation of
the simultaneous algebraic equations and the solution thereof by using the
Thomas algorithm are not given here.
-------
29
3.2. RESULTS AND DISCUSSIONS
The Langmuir type isotherm given in equation (23) is plotted in
' -6 '
Figure I for A = 1.35 x 10 and A = 15.04. This Isotherm is employed
throughout this study. Figure 2 shows the adsorhate concentration dis-
tributions in a packed bed adsorber for different values of oper.iting
time. The adsorbate concentrations in the gaseous and solid phasas of the
bed are initially zero. When adsorbate laden gas is introduced, the adsorbate
penetrates into the void in the bed by convection and diffusion, and simul-
taneously the adsorption process takes place between the adsorbate in the
void and the surface of the adsorbent. This results in the gas phase adsor-
bate concentration profile decreasing in the axial direction of flow. As
time increases, the adsorbent surface is gradually saturated and the adsorbate
concentration in the gaseous phase becomes higher. As T approaches infinity,
the adsorbent is completely saturated and the exit concentration becomes
the same as the inlet concentration, At the same time, the adsorbate
concentration on the adsorbent assumes the equilibrium value with resspect
to the inlet concentration at the inlet temperature. The effect of dispersion
results in the adsorbate concentration drop at the entrance of the bed as
shown in Figure 2. The magnitude of the concentration drop depends on the
intensity of dispersion expressed in terms of the Pec let number and the
magnitude of the concentration gradient.
Figure 3 shows the temperature distributions of the gas and solid phases.
The temperatures are assumed to be initially Identical with the room tempera-
ture (or the inlet gas temperature). Heat released from the adsorption
process raises the adsorbent temperature as well as the gas phase temperature.
The maximum gas and solid phase temperatures occur initially at the entrance
-------
30
:ig. I. Adsorption isotherm plotted according to a
Langrnuir type isotherm, equation (23)
(pcrarnsfsr, V).
-------
31
1.0 =
0.8
crjcr 0.6
n
>-
n
X
0.2
rig. 2. AclscrbatG conccn-l-ravion disiribution in a pnck
bsd cdscrber (R=5 , Ka=20, H =100, a=0.00o,
/5 = O.COI , / = 0.002 , pcrarnetar, r ).
-------
32
II
ID
1.14 -
-1.12 -
10
Fig. 3.
Temperature distribution in a paclod bed r/dscf'.,
(Si =5, Ke='^0,M-!00, a -0.005, ;3- 0.001, /-:0.(>/^
pcrcmsrer, -).
-------
of the bed and gradually move in the directton of gas flow as the zone of
maximum adsorption rate moves in the same direction. The maximum p,ns tempera-
ture always appears at a distance farther down the bed than the maximum
adsorbent temperature due to the convection 4>f heat in the gas phase in the
direction of flow. The effect of dispersion on the jump in the gas tempera-
ture at the entrance can also be observed in Figure 3. The temperature
gradient in the gas phase generated by the heat of adsorption causes heat
to be dispersed in the directions along and opposite to the gas flow. Since
no heat is transported out of the bed into the entrance section, heat dispersed
in the direction opposite to the gas flow is reflected into the bed at the
entrance. This renders the gas phase temperature at the entrance of the
bed to be higher than the incoming gas temperature. This phenomenon is
especially pronounced at the onset of the operation. When time T approaches
infinity, the bed temperature becomes the same as the incoming gas temperature
because the rate of heat generation decreases with an increase in the rlegrc-e
of saturation of the adsorbate on the adsorbent, and the heat generated is
rapidly removed by the gas flowing through the bed,
The effect of dispersion as characterized by the Peclet number on the
concentration in the gas phase of the bed at T = 100 for different values of
the heat of adsorption is shown in Figure A, and that in the solid phase in
Figure 5. As expected, these figures show that the adsorbate concpntration
are uniform throughout the bed when Pe = 0 (complete mixing). For large values
of Pe,e,g, Pe = 500, the flow behavior is essentially that of the plup, flow.
For intermediate values of Pe, namely for a finite degree of dispersion,
the adsorbate concentration profiles fall between the profiles for complete-
mixing and that for plug flow. The effect of heat of adsorption is also
clearly shown in the figures. Figure 4 shows that, for the same value of
the Peclet number, the average adsorbate concentration in the gas phase is
-------
34
0|0
it
X
1.0
OS
06
0.4
0.2
/ = 0
/ = O002
7 = 001
500
0.2
04
06
0.8
10
Fig. 4. Effect of Peclet number on the gas phase adsorbale
concentration distribution in a packed bed adsorber
at r=IOO (K.3-20, hHOO, a = 0.005, ,8 = 0.001 }
Parameter, P3 ).
-------
35
0
/ =0
7 =0002
/ =0.01
500
>- 0.4
Fig. 5. Effect of Peclet number on the solid phase adsorbate
concentration distribution in a packed bed adsorber at
T = IOO (Ka=20, H=IOO, a=0.005,£=0.00l; parameter, F
-------
36
lower for the Isothermal case (Y = 0) than for the non-isothermal case
(Y > 0). Conversely, Figure 5 shows that the average adsorbate concentration
in the solid phase is higher for the isothermal, case than for the non-
isothermal case. In other words, the adsorption process proceeds faster
in an isothermal bed than in a non-isothermal bed. This is because the
heat generated from the adsorption process in a non-isothermal bed raises
the solid phase temperature, thus resulting in a smaller driving force for
adsorbate transfer.
The effect of dispersion on the temperature distributons in the gas
and solid phases in the bed Is shown in Figure 6. For Pe = 0 (complete
mixing),' the temperature profiles are flat across the bed as expected, The
solid phase temperature is higher than the gas phase temperature because
heat is generated in the solid phase, raising the solid phase temperature
t
first, and then is transported to the gas phase. When the Peclet number
i jreases, the temperatures in both phases increase sharply near the entrance
and then level off. For very large values of the Peclet number, e.g. Pe = 500,
the temperatures drop sharply near the exit. This is reasonable since little
adsorption has occurred near the exit as reflected by Figures 4 and 5.
Figure 7 shows the effect of dispersion on the breakthrough of the
Incoming gas. For small values of the Peclet number, the dispersion of the
gas is so intensive that the adsorbate is almost uniformly distributed in
the bed. The adsorbate concentration ir. the gas phase near the exit is
almost the same as that near the entrance. Therefore, the adsorbate breaks
through the bed fairly rapidly. For large values of the Peclet number,
however, the gas is not well dispersed. The bed is saturated with the
adsorbate progressively from the entrance toward the exit. The adsorbate does
not move downstream either by convection or by diffusion unless it finishes
saturating the portion of the bed it has contacted. Thus a moving front is
-------
37
ii
>
it
ID
114
112
:ig. 6. effect of PscSet number on rhe tempernmrc?
distribution in a packed b-'jd adsorber ar /- =
IOO(Ke=20, MHOO,Q = Q005, /Q= 0001, / =0002;
pararnatsr P8 ).
-------
38
it
x
1.0
0.8
0.6
0.4
0.2
0
7=0
y = 0.002
X / / /
250
SOO
Rg. 7. tffect of Fsclet number on the exit adscrbute
concentration change in a packed bed adsorber,
(Ka =20, H =100, a =0.005, /3=0.001; parameter, P,).
-------
39
formed which separates the bed into two distinct portions: one witli complete
contamination and the other no contamination. In this manner, the hre.nk-
through occurs relatively late and sharply. It is worth noting that, for
the same value of the Peclet number, the breakthrough occurs earlier for the mm-
isothermal process than for the isothermal process.
Figure 8 shows the effect of dimensionless external mass transfer
coefficient, K , on the adsorbate concentration distribution. For K = 0,
no adsorption takes place in the bed, and therefore, the void space of the
bed is completely filled with the incoming gas and the adsorbent remains
uncontaminated. For K values other than zero, the concentrations of both
the gas and solid phases in the bed are higher for large values of K
e
than for small values of K since the bed is saturated more rapidly for
large value of K ,
Figure 9 shows the effect of a, the inverse of the adsorption capacity
of the bed, on the transient adsorbate concentration at the exit for three
different values of the heat of adsorption. For a = 0, or I/a -> °°, the
bed has infinite adsorption capacity and is never saturated. For large
values of a, or small values of I/a, the adsorption capacity is small:
therefore, the bed is rapidly saturated. The effect of a on the solid phase
temperature distribution in the bed is shown in Figure 10, For small vnlues
of a, more adsorbate can he adsorbed and more hent is generated in the heel.
This may result in very high temperatures in the bed. Tn particular, for
a = 0, the bed temperature may rise continuously with time until heat genera-
tion is equal to heat removal by gas flow. In this case, the adsorber
temperature may rise to a very high level, and consequently the stability
problem becomes serious.
-------
crjcr
it
o|o
II
X
10
0.8
0.6
0.4
0.2
X
Y
0 (for X )
20
_20_
'— -- . 2
Otlor Y )
o
0.2
0.4
0.6
08
0
rr
I
i-ig. 8. Effect of K* on ma cclsorbats concentration
distribution in a paclod bed adsorber at
T = IOO(R = 5, h! =IOO,a=Q005, ,3=0.001, /=0.002;
pcrcmatsr, K. ).
-------
10
08
, E
cr|cr 06
ii
>-
0.4
02
0
O
7 = o r = o
/ = 0002 i i i i i i—+-- / = OOO2
7 = 001 7=001
50
100
ISO
200
25O
30O
rig 9. Effect of a on the c.-.it adsorbole conctniidiicn
chcnge in a poclod bed adsorber (Pa =5, K- -?0,
H = IOO, ,3=0001;
-------
42
I
>
22
20
18
16
12
\
\
\
\
\
\
at r
at r
100
300
\
N
- ocoz
0005
^___ I • ~--~—
Fig. 10. hjfsct of a en fhe solid phase temper iture
fllsfrlbupon in a oock^d bed adscrc :-r (P? •:•),
K-..-20, M = IOO, /3= OOCI, y-0002; pc^fr/-;-^,
-------
43
A further Insight into the operation of an adsorber unit can he
gained through evaluation of accumlated adsorption efficiency. A macro-
scopic adsorbate balance over the total volume of the bed Rives
t L L
Gt = / C C dt + f C H0 dz + f q H dz (36)
0 e 0' g n" s
By introducing dimensionless quantities in equation (18), equation (36)
can be rewritten as
T 1 1
T = / X di + f X dX + - / Y dX ifaj^O
o e o' a o
or (37)
T 1
T=/XdT+/XdX if u = 0
0 e 0
Thus the accumlated adsorption efficiency can be defined as
na = 1 - i / Xe di (38)
or (39)
1
, .
-{/XdX+-/YdX}
T °
n
3 0 0
= — JXdX ifa = 0
0
Note that the adsorption efficiency changes with time and c?m be obtained by
integrating either equation (38) or (39) numerically. Table ] shows the
accumulated removal efficiencies for the nominal case at different times.
The computational results by using both equations, viz. equations (38) and (3°)
-------
44
Table 1. Accumulated adsorption efficiency for the nominal standard
case.
time, T
50
100
150
200
250
300
adsorption efficiency, n
3
equnticn (38)
0.9930
0.8436
0.6001
0.4607
0.3762
0.3197
equation (39)
0.9874
0.8422
0.5998
0.4606
0.3760
0.3196
-------
45
are almost identical, indicating that the numerical scheme empJoyed in
this study is reliable.
Figure 11 shows the effect of axial dispersion characterized by the
Peclet number on the accumulated adsorption efficiency. The adsorption
efficiency is generally increased when dispersion is less significant and
vice versa. In all cases, the accumulated adsorption efficiency decreases
as time increases because the bed becomes saturated gradually. The effect
of heat of adsorption, Y> is also shown in the figure. Jt is readily seen
that the accumulated adsorption efficiencies are lower for the nonIsothermal
cases (y > 0) than for the isotherma] case (y = 0).
The effect of the inverse adsorption capacity a on the accumulated
adsorption efficiency at different values of Y is shown in Figure 12. When
a is small the adsorption capacity of the bed is large, resulting in slow
saturation of the bed and consequently, in a high accumulated adsorption
efficiency.
-------
46
I.O
0.8
0.6
0.4
0.2
0
0
100
200
300
Fig. II. Effect of Feclet number en j-he accumulated
cdscrbats removal efficiency (Kj=20, !-i-100,
G = 0005, &---0.001; parameter, P* ).
-------
47
10
08
06
0.4
02
0 -
0
-7=0
T- X=0002
/=O.OI
— —POO?
100
200
oOO
Fig. 12.
Effect of a on the accumulated arlscrbnte
rsmoval efficiency (R =5, K.-20, H-IOO,
/5=OOOI; parameter, a ).
-------
48
NOMENCLATURE
available external surface area per unit volume of bed,
2. 3
cm /cm
A- = constant ( K)
' cfAl
A.. = constant, •=-
-------
49
H = gas phase hold-up, i.e., mass of gas per unit volume of bed,
&
3
g of gas/cm of bed
H = solid phase hold-up, i.e., mass of adsorbent per unit volume of bed,
s
2
g of adsorbent/cm of bed
AH = average heat of adsorption, cal/g
3.
k = external mass transfer coefficient based on external surface of
e
particle and concentration driving force, cm/sec
(
K = d line sf.on less adsorbent heat conductivity,
L H
S
k ap L
6 o
K = dlmenslonless mass transfer coefficient, c~
L = depth of adsorption bed, cm
Pe = Peclet number
Pe, = Peclet number for heat transfer, GL r
n din F.
PT
Pe = Peclet number for mass transfer, -——
m Op E,
g 1
q = amount of adsorbate adsorbed per unit mass of adsorbent, g of
adsorbate/g of adsorbent
q = maximum amount of adsorbate which can be adsorbed per unit mass of
adsorbent, g of adsorbate/g of adsorbent
= overall rate of adsorption per unit volume of bed, g/sec-cm
t = time, sec
T = adsorbent temperature, K
d.
T = gas temperature, K
5
Tn = temperature at the inlet of the bed, K
T
U = dimensionless gas temperature, •=&•
0
R
-------
*
50
T
**
V = dimensionless adsorbent temperature, —
L0
X = dimensionless adsorbate concentration in gas phase, —
cf
A C
X = dimensionless adsorbate equilibrium concentration in gas pahse, —
cf
Y = dimensionless adsorbate concentration in solid phase, —
m
z = axial distance from entrance of bed, cm
GREEK LETERS
H_c
a = inverse of the adsorption capacity of the bed,
s m
B = ratio of heat capacity of gas phase to that of solid phase in the
H c
s s
dimensionless heat of adsorption,
accumulated adsorption efficiency
2
= dimensionless axial distance, —
Li
P = density of gas, g/cm
O
tG
T = dimensionless time, T »
L H
g
void fraction of the bed
c H J
s s 0
-------
51
REFERENCES
1. Masamune, S. and J. M. Smith, ALChE Journal, 10, 246 (1964).
2. Rimpel, A. E., Jr., D. T. Camp, J. A. Kostecki, and L. N. Canjar,
AIChE Journal, 14, 19 (1968).
3. Brunauer, S., "The Adsorption of Gases and Vapors, Volume I, Physical
Adsorption," Princeton University Press, Princeton, N. J. (1943).
4. Young, D. M. and A. D. Crowell, "Physical Adsorption of Gases,"
Butterworth, London (1962).
5. Deans, H. A. and L. Lapidus, AFChE Journal, 6, 656 (1960).
6. Wen, C. Y. and L. T. Fan, "Models for Flow Systems," Monograph to be
published, Gordon and Breach, New York (1974).
7. Lee, R. G. and T. W. Weber, Can. J. Chem. Eng., 47^, 54 (1969).
8. Gariepy, R. L. and I. Zwiebel, "Adsorption of Binary Mixtures in Fixed
Beds," a paper presented at the 68th National Meeting of the AIChE,
Houston, Texas, Feb. 28 - March 4 (1971).
9. Thomas, W. J. and J. L. Lombardi, Trans. Instn. Chem. Engrs., 49, 240
(1971).
10. Carter, J. W. and H. Husain, Trans. Instn. Chem. Engrs., 50, 69 (1972).
11. Carter, J. W., Trans. Instn. Chem. Engrs., 44, T253 (1966).
12. Meyer, 0. A. and T. W. Weber, AIChE Journal, 13, 457 (1967).
13. Lee, R. G. and T. W. Weber, Can. J. Chem. Eng., 47., 60 (1969).
14. Schneider, P. and J. M. Smith, ALChE Journal, 14^ 762 (1968).
15. Chu, C. and L. C. Tsang, Ind. Eng. Chem. Process Des. Develop., 10,
47 (1971).
16. Cooney, D. 0. and F. P. Strusi, Ind. Eng. Chem. Fundam., 11, 123 (1972).
17. Tada, K., S. Shikagawa, and I Nakamori, a paper presented at the 37th
annual meeting of the Society of Chemical Engineers, Japan, Nagoya,
Japan, April (1972).
18. Gupta, S. P. and R. A. Grecnkown, a paper presented at the 72nd National
Meeting of the AIChE, St. Louis, MO., May 21-24 (1972).
19. Liu, S. L. and N. R. Amundsen, Lnd. Kng. Chem. Fundamentals, 2, 183 (19f>'J)
-------
52
20. Paris, J. R. and W. F. Stevens, Can. J. Chera. Eng., 48, 100 (1970).
21. Feick, J. and D. Quon, Can. J. Chem. Eng., 4£, 205 (1970).
22. Lapidus, L., "Digital Computation for Chemical Engineering," McGraw-
Hill Co., New York (1962).
23. Smith, G. D., "Numerical Solution of Partial Differential Equations,."
Oxford University Press, Oxford (3965).
-------
53
4. GASEOUS POLLUTANT REMOVAL BY A SINGLE BED CYCLIC ADSORBER WITH SYNCHRONOUS
THERMAL CONTACT
The adsorption process has been employed mostly In the separation
of fluids and solvent recovery (Treybal, 1968). The adsorption process
has also been increasingly employed for pollutant removal from air (Faulkner
et al. 1973). An adsorption unit usually consists of one, two or more
fixed-bed adsorbers (Danielson, 1967; Stern, 1968). To remove the pollutant
(the adsorbate), a pollutant laden air stream can be passed through an
adsorbent-packed bed or beds wherein the pollutant is concentrated.
The adsorption process is continued until the effluent stream from the
bed reaches the threshold or maximum allowable concentration. At this
point the concentrated pollutant must be disposed. The disposal of the
pollutant may be effected in any of the following ways: (1) The adsorbent
along with the pollutant is discarded. (2) The pollutant is desorbed and
either recovered, if it contains valuable components, or discarded.
(3) The pollutant is oxidized on the adsorbent surface and removed.
Among the methods of disposing the concentrated pollutant, the on-site
(or in-system) desorption which gives rise to a cyclic operation appears to
be most practical, because this method has the following advantages over
other methods: (1) No handling of solids is needed during operation.
(2) No replacement of the adsorber is necessary. (3) The adsorption-
desorption cycles are repeated continuously. The last point is of particular
Importance for those situations where the pollutant is generated all the
time. To achieve a continuous cyclic operation, usually two or more adsorber
beds are used (Stern, 1968; Mattia, 1972). However, as is shown in this
paper, a single bed adsorber can also handle the continuous pollutant
flow effectively. The primary aim of the present study is to show the
feasibility of such a single bed adsorber-desorber system (or simply single
bed adsorber system) and understand its performance through computer
-------
54
simulation. Such a compact syotem can be Installed in restaurants,
laundries, foundries, laboratories, painting rooms, workshops, mines,
etc. It can also find application in space ships and submarines due to
its compact character.
Cyclic adsorption-desorption processes^ for fluid seperation have
been studied by several investigators. Wilhelm et al. (1966, 1968)
and Sweed and Wilhelm (1969) first introduced the concept of parametric
pumping. Parametric pumping is a cyclic separation process in which two
synchronous actions a periodic temperature variation and an alternating
fluid flow are imposed on a bed of adsorbent. The alternating fluid
flow through the adsorber is coupled with cycling of temperature levels,
thus causing a build-up of separation from cycle to cycle. Such a system
is a closed system in which the fluid mixture flows between two reservoirs
at two opposite ends of the adsorber. There is neither feed introduced
nor product withdrawn during the cycles until the separation is complete.
This is equivalent to a batch process. Gregory and Sweed (1970, 1972) and
Chen et al. (1971. 1972) later modified it by continually introducing the
feed and withdrawing the product during portions of a cycle. As for the
mathematical model of the adsorption process, Pigford et al. (1969)
assumed an equilibrium theory while Gupta and Sweed (1972) presented a
more realistic non-equilibrium theory. Recently, Kowler and Kadlec (1972)
considered the separation of a gaseous mixture in a fixed bed adsorber
by cyclically regulating the pressure gradients in the bed. For the pollution
control oriented adsorption system presented here, some operational
schemes based on a concept similar to the parametric pumping with thermal
contact are incorporated. These schemes are to be arranged so that the
continuous flow of the pollutant laden air stream is possible.
-------
55
The desorbed pollutant may be scrubbed by water or It can be burned
and disposed. Since water scrubbing usually requires a large scrubbing
tower and may cause water pollution (Faulkner, 1973), it is not desirable
for the compact system under consideration. In the present system the
desorbed pollutant is burned into harmless gases and thus an incinerator
is included in the system.
In the following, the operational schemes of the system under consideration
are first described. The mathematical model for the adsorber is then
formulated and the effects of some significant parameters on the performance
of the system are investigated by computer simulations.
-------
56
4.1. OPERATIONAL SCHEMES
Two operational schemes are proposed here. One uses fresh air for
desorption and the other uses exhaust gas, as shown in Figures 1 and 2,
respectively. The adsorber is packed with a bed of activated carbon.
Activated carbon is used as adsorbent because it is very effective in
adsorbing different organic molecules, even from a humid gas stream
(Stern, 1968; Hassler, 1967). The adsorber is embeded with a coiled tube
for cooling or heating purposes (Alternatively, the adsorber can be embeded
with parallel tubes in a manner similar to a shell and tube heat exchanger).
It is assumed that the temperature in the bed can be kept uniform by
means of the tube (or tubes). The jacketed incinerator is used to burn the
pollutant during the desorption period and it also serves as a heat exchanger.
At the beginning of a cycle, the adsorber bed is cooled to a
desirable temperature by flowing a cool fresh air stream or cold water
through the coiled tube as shown in Figures 1 and 2. While the bed is
kept cool, the pollutant laden air stream (henceforth called feed) flows
through the bed from top to bottom. Initially, the adsorbent is relatively
clean so that the pollutant is almost completely adsorbed. Consequently,
the effluent air stream is virtually free of the pollutant and can be
ejected to the atmosphere. As adsorption continues, the adsorbent becomes
increasingly saturated and the pollutant concentration in the effluent
stream increases gradually. When the effluent concentration reaches the
maximum allowable concentration, the adsorption process is interrupted
and the system is switched to the desorption phase. A plot of the effluent
pollutant concentration versus time is called a breakthrough curve and is
illustrated in Figure 3 where c. is the feed concentration and C is the
f • max
maximum allowable concentration. Thus, when the effluent concentration
-------
Scheme
57
Pollut0d_Air ^
Fan
i
J
**l
02
r
to atmosphere
1 * ~
^-U Coot Air
L. iii
]
z=0
(X=o)
-Adsorbent
z=L
(X = l)
r ^' ^ AV
Incinerator
tubes or
coils
fresh air
Fan
• to atmosphere
to atmosphere
Flow Paths during adsorption
Flo'.y Paths during ('.:sorption
Fig !. A single adsorber system using fresh air for desorpticn.
-------
58
Scheme H
Polluted
Air
Vent
Atmosphere
• Flow paths during adsorption
- Flow paths during desorption
Fig. 2. A single adsorber system using exausted air for
desorption.
-------
O
k_
c
-------
60
reaches C , the feed is diverted to the incinerator where it is burned
max
together with the desorbed pollutant. It is assumed that the capacity of
the incinerator is large enough so that the pollutant can be burned almost
completley. Thus the exhaust from the incinerator is free of the pollutant.
The desorption process can be effected by two different schemes.
These are distinguished as scheme I in Figure 1 and scheme II in Figure
2. In scheme I a portion of the exhaust gas from the incinerator is
allowed to flow through the coiled tube to raise the bed temperature.
At the same time, a fresh air stream flows through the jacket of the
incinerator. The heated fresh air stream then flows upward through the
bed to desorb the pollutant. The desorbed pollutant stream combines with
the original pollutant laden stream before entering the incinerator.
The desorption process is stopped when the bed has been cleaned to a
certain level (This point will be detailed later). This completes one
aosorption-desorption cycle. Thus, within a cycle, the direction of
flow is changed synchronously with the change of bed temperature.
Scheme II is a modification of scheme I. It differs from scheme I
in that it does not require an additional fresh air stream for desorption.
The exhaust gas stream from the incinerator is divided into two streams;
one is used to heat the adsorber through the coiled tube and the other to
desorb the pollutant. Since it is assumed that the exhaust gas is
essentially free of pollutant, it can be considered as an inert gas and
thus has the same desorbing property as fresh air. Note that the feed stream
is heated in the incinerator jacket before it combines with the desorbed
polluted stream. Thus, the heat loss due to mixing is reduced.
In comparing the two schemes described above, it appears that Scheme II
is more advantageous than scheme I because no additional air stream is
-------
61
required and heat loss due to mixing is reduced. Furthermore, In scheme
II, an inert gas is used for desorption. This can prevent the activated
carbon in the bed from being oxidized. Scheme II, however, does have some
disadvantages. The stream entering the incinerator is diluted due to
mixing of the desorbed stream with the feed stream (see Figure 2), and
this dilution may require excessive thermal energy for Incineration of the
pollutant. Moreover, if the exhaust gas from the incinerator contains a
substantial amount of partlculates, the exhaust gas stream should pass a
filter before entering the adsorber.
-------
62
4.2. MATHEMATICAL MODEL OF THE ADSORBER
The assumptions made in deriving the performance equations of the
single adsorber system under consideration are:
(a) The adsorption process takes place isothermally at a lower
temperature and the desorption process takes place isothermally
at a higher temperature.
(b) External mass transfer is the rate controlling step. The model
of mass transfer based on this assumption is called the film model.
(c) Parameters such as mass transfer coefficient, porosity of bed,
adsorbent density, specific surface area of adsorbent, etc.. do
not change with respect ot operating conditions.
(d) No dispersion of the gaseous components occurs in the entrance
and exit sections adjacent to the bed, although the existence of
dispersion within the bed is not neglected.
Under these assumptions, the following differential equations can
be written by taking mass balances on the adsorbate and the adsorbent.'
2
- e P D ^-f + G |£ - k a po (c - c*) (1)
g 2 9z eg
ke a pg (C ' C*>
The ambiguous sign In equation (1) accounts for the direction of the
gaseous flow. The positive direction is that from top to bottom. In other
words, the positive direction in the bed is always measured from the top. Thus,
the "-" should be used during adsorption while the "+" should be used
during desorption. In equations (1) and (2), c* is the gas phase equilibrium
concentration which is related to q by a Langmuir type isotherm
-------
63
b.c*
where q_ is the amount of adsorbate on unit mass of adsorbent when the
adsorbent is fully covered by a monolayer of the adsorbate. The constant b
is determined from (Brunauer, 1943)
exp(A,/T)
Z— (4)
T5
where AI and A are constants and T is the temperature of the adsorber bed.
Let the over-all time or period of each cycle be t , the adsorption
time t , and the desorption time t,. It is assumed that the switching from
& Q
adsorption to desorption is instantaneous so that t = t + t,. Because of
the cyclic steady state nature of the operation, the initial conditions
of the adsorption process are those at the end of the desorption and vice
versa. These conditions along with the appropriate boundary conditions
for equations (1) and (2) can be expressed mathematically as shown
below, noting that the directions of flow are opposite to each other during
the adsorption and desorption processes.
During adsorption
c (0,z) = c(tc , L - z) (5)
q (O.z) = q(tc~, L - z) (6)
c (t,0) = c, +1^- 8c(t» °>
'£ G 8z
3c (t. L)
-------
64
During desorption
c(t """, z) = c(t ~ L - z)
a 3
q(ta , z) = q(ta~» L - z)
ctt.L, .
3z
(t, 0) = 0
t < t < t
- ^ a - - c
(9)
(10)
(11)
(12)
In the above equations c is the inlet concentration of the pollutant in
the desorbing air stream. For either scheme, c is zero since the
desorbing stream contains no pollutant, t indicates the end of thp
3.
adsorption period, t , the beginning of the desorption period, and t the
3
end of the desorption period. The temperature, T, in equation (4)
takes on T for adsorption and T, for desorption.
Equations (1) through (12) can be rewritten in dimensionless forms
by introducing the following dimensionless quantities.
X = —
~Cf
tG
L H
Fe
GL
EpgD
-------
65
k a p_ L
K = -S 8.
e G
H cf
s Tn
B = b cf
The resulting govering equations are
f
|i - K (X - X*) (14)
where X* is determined from the equilibrium condition
BX*
(15)
1 + BX*
The corresponding dimensionless initial and boundary conditions are,
during adsorption
X (0, X) = X(TC , 1 - X) (16)
Y (0, X) = Y(TC", 1 - X) (17)
v (r m - i ^ 1- aX(T,0)
X (T, 0) - 1 4 — --^-
i
i
i 0 < T < T
'> ' - - a
JliII = o (19)
3X U J
-------
66
during desorption
X (T , A) = X (T ", 1 - A) (20)
3. 3.
Y (T + A) = Y (T ', 1 - A) (21)
a a
X (T, 1) = - T (22)
» T < T < T
'a - - c
3X (x.O) _ J (23)
8A ~ U
Equations (13) through (15) together with equations (16) through (23)
cannot be solved analytically because of the nonlinearity appearing in
equation (15). They, can be solved however, by the finite difference
method (Ames, 1969). It should be noted that the solutions for schemes I
and II are identical although there is a practical difference in operation
between the two schemes as described previously.
-------
67
4.3. RESULTS OF SIMULATION AND 1)1 SCUSSTON
The performance of the adsorber system under consideration Is examined
with respect to significant parameters such as:
(1) pollutant concentration in the feed,
(2) maximum allowable concentration,
(3) adsorption temperature,
(4) desorption temperature,
(5) linear velocity of the gas flow,
(6) residual pollutant loading at the end of desorption, and
(7) extent of the axial dispersion characterized by the Peclet number.
The first parameter depends on the content of a pollution source. The second
parameter is related to human tolerance toward the pollutant and is
regulated usually by emission standards. The other parameters are subject
to a desinger's choice. Thus it is desirable to examine effects of each
parameter on the system performance. As a basis for comparison, the results
of simulation For a set of nominal values of the
parameters are first presented and discussed. The effects of each parameter
are analyzed subsequently.
The numerical values of the nominal conditions are listed in Table 1.
Additional constants employed in the simulation are listed in Table 2.
Under these conditions, the dimensionless quantities K and a are,
for adsorption, K =45.0
a = 1.046 x 10~6
for desorption, K =37.46
a = 8.71 x ID"7
-------
68
Table 1. Numerical Values of Nominal Conditions
(1) Cf, feed concentration 500 ppm
(2) C , maximum allowable concentration 25 ppm
max
(3) T , adsorption temperature 25°C
a
(A) T , desorption temperature 70°C
(5) P, pressure in the adsorber 1 atm
(6) u, superficial linear velocity of gaseous flow 40 cm/sec.
(7) (1, residual pollutant loading at the end of desorption 5%
(8) Pe, Peclet number 200
-------
69
Table 2. Additional Constants Employed in the Simulation
a = 15 cm /cm
^ = 0.2312 x 10~3 (°H
A2 = 0.44076 x 104 °K
D = 30 cm.
a
d = 0.4 cm.
P
k = 3 cm/sec.
e
L = 40 cm.
qm = 0.5 g/g
<: =0.4
p = 0.75 g/cm
s
-------
70
In this study, the direction of flow during desorption is opposite
to that during adsorption. This is due to the fact that at the end of
adsorption, a pollutant concentration gradient exists in the bed where the
upper portion is almost saturated while the lower portion is relatively
clean.. If desorption were conducted in the same direction, some of the
pollutant which has been desorbed from the upper portion would be
readsorbed in the lower portion, thereby hindering the desorption process.
If desorption were conducted in the opposite direction this phenomenon
would not occur.
Figures A and 5 show the distributions of the pollutant concentrations
in the gas and solid phases, respectively, during the adsorption period.
It can be seen that at the early stage of adsorption, only a narrow
zone near the top end is contaminated. As the period of time increases,
the pollutant concentrations in both the gas and solid phases increase
at every point. Of particular Interest is the increase in the gas phase
at the exit (A « 1) as shown in Figure 6. The effluent concentration is
essentially free -of pollutant for approximately 26 minutes, after which it
increases very sharply. As soon as the maximum allowable concentiation
(in this case, 25 ppm) Is reached, the adsorption operation is interrupted.
The amount of pollutant loaded on the adsorbent can be obtained by integrating
AL/1 YfAdA (24)
where Y,. is the solid phase pollutant concentration profile at the
termination of adsorption. Note that the quantity
fl Y dA
0 fA
ia represented by the shaded area in Figure 5.
-------
71
x-t
Fig. 4 Cos phase pollutant concentration during adsorption
period (Nominal conditions; parameter: time,min.).
-------
72
.020-
.016
.012 -
V
Y~"c;
.008-
.004-
1.0
Fig. 5 Solid phase pollutant concentration during adsorption
period (Nominal conditions; parameter: time, rnin.).
-------
.05
.04
.03
x =
.02
.01
0
10
20
max. auowauie cone. a
is reached /
/
/
/
_4 — i I i i
30 40 50 60 7
'/o
I/ i
0 80
Time , min.
Fig. 6 Effluent pollutant concentration during adsorption period (Nominal conditions).
-------
74
As soon as adsorption is terminated, desorption is initiated.
During the desorption operation, the pollutant concentrations in the gas
and solid phases decrease as shown in Figures 7 and 8, respectively.
Since the desorbing air stream flows upward, the pollutant is desorbed
faster in the lower part (larger X) than in the upper part (smaller X).
Desorption is terminated when the residual pollutant loading on the adsorbent
is at a certain fraction (in the nominal case, 5X) of the original
loading,i.e., Q.. The amount of the residual pollutant on the adsorbent
can be obtained as
Q2 - pg (1 - c) ^ AL /J YfD dX (25)
where Yf_ is the solid phase pollutant concentration profile at the end
of desorption. As before, the quantity
is represented by the shaded area in Figure 8.
The capacity of adsorption per cycle is defined as the difference
between the original loading and the residual loading. Let the capacity
be denoted by AQ. Then
Q1 - Q2 (26)
This quantity divided by the time of a cycle gives the pollutant removal
rate of the adsorber. The adsorption time or period, desorption time,
capacity per cycle, and removal rate of the adsorber along with the values
of the parameters are tabulated in Table 3. These values for the nominal
-------
75
X =
Cf
x =
JL_
L
Fig. 7 Gas phase pollutant concentraticn during desorption
period (Nominal conditions, parameters : time , min.).
-------
76
Y= -J-
direction
of flow
o.o
0.2
0.6
0.8
1.0
Fig. 8 Solid phase pollutant concentration during desorption
period (Nominal conditions, parameters : time, min.).
-------
Table 3. Effects of Various Parameter on Adsorber Performance
No.
1
2
3
4
5
6
7
8
9
]0
]1
12
13
14
15
16
17
Cf
ppm
300
©
^oo)
500
500
500
500
500
500
500
500
500
500
500
500
500
500
max
ppm
25
25
25
(10)
©
25
25
25
25
25
25
25
25
25
25
25
25
par<
T
a
°C
25
25
25
25
25
©
©
25
25
25
25
25
25
25
25
25
25
unetei
Td
°C
70
70
70
70
70
70
70
©
@
70
70
70
70
70
70
70
70
•s
P
atm
1
1
1
1
1
1
1
1
1
©
©
1
1
1
1
1
1
u
cm/s
40
40
40
40
40
40
40
40
40
40
40
@
©
40
40
40
40
6
%
5
5
5
5
5
5
5
5
5
5
5
5
5
©
©
5
5
Pe
No.
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
©
0
adsorption
time,
min.
70.3
79.5
62.5
60.5
79.3
89.4
55.7
70.3
70.3
140.7
35.2
98.3
53.7
75.1
63.9
65.2
83.6
desorption
time,
min.
13.8
14.6
13.0
12.7
14.6
13.6
14.0
20.5
9.5
27.2
6.8
18.1
11.2
17.6
11.7
13.2
19.8
fraction of
desorption
operation
0.164
0.155
0.172
0.173
0.155
0.132
0.201
0.226
0.119
0.162
0.162
0.155
0.173
0.190
0.155
0.168
0.191
capacity
nf
adsorption
g/cycle
68.9
38.5
123.3
59.9
76.8
89.2
53.7
69.0
68.9
68.9
68.9
72.3
65.8
73.9
62.9
64.3
78.9
removal
adsorber
g/min.
0.820
0.409
1.633
0.818
0.818
0.866
0.770
0.760
0.863
0.410
L.640
0.621
1.014
0.797
0.832
0.820
0.763
-------
78
case are contained in the first row. Starting from the second row,
one parameter each is varied from the nominal values. The values which
deviate from the nominal values are encircled.
The effects of the various parameters on the adsorber performance
are discussed in what follows.
(1). Feed Concentration
The results in Table 3 show that the removal rate of the adsorber is
almost proportional to the feed concentration. However, the cycle time
decreases with increasing feed concentration but the fraction of time for the
desorption operation increases with Increasing feed concentration.
Hence a higher feed concentration needs more frequent desorption.
Furthermore, a higher feed concentration is usually achieved by applying
pressure. Higher pressure in the adsorber not only increases the power cost
bui_ also adds construction cost. Therefore, a higher feed concentration
has no advantage for the cyclic operation.
The mathematical model is simulated for two different feed concentrations,
one lower and one higher than the nominal values, keeping all other
parameters unchanged. The results are presented in row 2 and row 3,
respectively, of Table 3. It is obvious that if the feed concentration
is lower, the pollutant removal rate is lower, and vice versa.
(2). Maximum Allowable Concentration
As mentioned previously, the maximum allowable concentration is
usually regulated by local emission standards. If a stricter emission
standard is imposed on the system, the maxlmun allowable concentration,
C should be lowered. Conversely, if the emission standard is slackened,
IQaX
C can be Increased.
max
-------
79
The pollutant removal rates for different values of C are almost
max
identical. However, the cycle time increases with incriMsing C , but
the fraction of time for desorption operation decreases with increasing
C . The results from the effect of this parameter are 'given in rows 4
and 5 of Table 3. It is interesting to note that the pollutant removal
rates for different values of C are almost identical although the
max °
adsorption time, desorption time, and adsorption capacities vary significantly.
(3). Adsorption Temperature
At the temperature of 20 , 25 , and 30 C, the adsorption times are
89.4, 70.3, and 55.7 minutes, respectively. These results indicate that
the adsorption process is very sensitive to the adsorption temperature.
The cycle time increases with decrease in adsorption temperature but
the fraction of time for the desorption operation decreases with decreasing
adsorption temperature. Moreover, the lower the adsorption temperature
the higher the removal rate of adsorber. Therefore, low temperature favors
pollutant adsorption.
At the nominal temperature, 25 C, the adsorption time is 70.3 minutes.
At 20 C, the adsorption time is 89.4 minutes, an increase of 27%. On the
other hand, if the adsorption temperature is 30 C, the adsorption time is
reduced to 55.7 minutes, a reduction of 21%. These results indicate that
the adsorption process is very sensitive to the adsorption temperature.
A similar observation can be drawn by comparing the pollutant removal rate
at different temperatures (see rows 1, 6, and 7 of Table 3).
(4). Desorption Temperature
It can be seen from Table 3 that the desorption process is also very
sensitive to temperature. At the temperature of 80, 70, 60°C, the
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80
desorption times are found to be 9.5, 13.8, and 20.5 minutes, respectively.
Logically, the desorptlon temperature should be as high as possible.
However, the cost of thermal energy and the thermal stability of the bed
constrain the maximum desorption temperature.
(5). Pressure
The results reveal that the adsorption time and desorption time are
almost inversely proportional to the pressure. However, the fraction of
time for the desorption operation is essentially independent of the pressure
in the range of operation. The results also show that the capacity per
cycle does not change with the pressure. Therefore, the removal rate of
the adsorber is proportional to the pressure. The operating pressure
depends on the purpose and situation of operation. From the viewpoint
of energy cost, the adsorber should be operated under the atmospheric
pressure except in a space ship or submarine where a lower or higher pressure
prevails naturally.
(6). Superficial Velocity of Gaseous Flow
The value of the linear velocity of gaseous flow given in Table 1
is selected at the adsorption temperature. If the same mass flow rate
of air Is maintained, the linear velocity during the desorption period is
higher than that during the adsorption period because the temperature
during the former is higher than that during the latter.
The recommended linear velocities for adsorption fall between 24
and 55 cm/sec. (Treybal, 1968). The nominal value is chosen to be
40 cm/sec.. As shown in Table 3, the adsorption time is relatively longer
but the desorption time is only slightly prolonged at a lower velocity.
On the other hand, the adsorption time Is shortened much more than the
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desorption time at a higher velocity. Most significantly, the pollutant
removal rate is much higher at the higher velocity. A desirable situation
is one where the linear velocity is low enough so that the energy for
transporting the gas is small and yet is high enough so that the high removal
rate is maintained.
(7). Residual Pollutant Loading at the End of Desorption
Lowering of the residual pollutant at the end of desorption prolongs
the desorption time. It is also prolongs the adsorption time and increases
the adsorption capacity. However, in terms of the pollutant removal rate,
this does not yield a higher value. As the results in Table 3 indicate,
the residual pollutant load should remain reasonably high in order to
maintain a high pollutant removal rate.
(8). Extent of Dispersion
Since
PT
Pe = ^ and G = up
e P D g
O
the Peclet number can be rewritten as
For the operating conditions under consideration, the Schmidt number
is approximately unity (see Appendix) and the Reynolds number is in the
neighborhood of 100. Under these conditions, the dimensionless group
D e/ud is approximately equal to 0.5 (Levenspiel, 1962) where d is the
P P
adsorbent particle diameter. Therefore,
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82
T ud _ T
_ uL p L . _ L
Pe = ;r— = ir-1- — = 2 T~
De De d d
The Peclet number can be perceived as depending only on the adsorber
length (bed depth) and the adsorbent particle diameter. The adsorption
and desorptlon times calculated using different Peclet numbers are shown
In Table 3. It can be seen that the higher the Peclet number or the
less the mixing, the longer the adsorption time. Thus, a higher Peclet
number is favorable because it requires less frequent desorption. However,
a large Peclet number must be achieved by using finer particles and/or
a longer adsorber. This gives rise to a higher pressure drop. Furthermore,
a large Peclet number does not yield a higher removal rate.
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83
NOMENCLATURE
2
A = cross-sectional area of the adsorber, cm .
2 3
a = available external surface area per unit volume of bed, cm /cm .
A.. = constant, ( K) .
A» = constant, K.
b = adsorption coefficient expressed in the Langmuir isotherm equation.
B = adsorption coefficient expressed in equation (15).
c = adsorbate concentration in gas phase, g of adsorbate/g of adsorbate
free gas.
c* = equilbrium concentration, g of adsorbate/g of adsorbate free gas.
c, = pollutant concentration, g of adsorbate/g of adsorbate free gas.
c = maximum allowable concentration, g of adsorbate/g of adsorbate
nicix f
free gas.
2
D = axial dispersion coefficient for mass transfer, cm /sec.
D = diameter of the adsorber, cm.
£1
d = adsorbent particle diameter, cm.
2
G = mass flow rate of fluid per unit cross-sectional area, g of gas/sec-cm .
H = gas phase hold-up, i.e., mass of gas per unit volume of bed, g of
S gas/cnr of bed.
H = solid phase hood-up, i.e., mass of adsorbent per unit volume of
bed, g of adsorbent/cm^ of bed.
k = external mass transfer coefficient based on external surface of
particle and concentration driving force, cm/sec.
k£ap L
K = dimensionless mass transfer coefficients, —°
e (j
L = depth of adsorber bed, cm.
P = pressure in the adsorber, atm.
GL
Pe = Pec let number, —
*cp D
g
Q = amount of adsorbate loaded on the adsorbent at the end of adsorption, g.
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84
Q. = amount of adsorbate remaining on the adsorbent at the end of
desorption, g.
AQ = Q, - Q2i capacity of adsorption, g.
q = amount of adsorbate adsorbed per unit mass of adsorbent, g of
adsorbate/g of adsorbent.
q = amount of adsorbate adsorbed per unit mass of adsorbent, when the
adsorbent is fully covered by a monolayer, g of adso'rbate/g of
adsorbent.
t = time, sec.
T = temperature, K.
T = adsorption temperature, °C.
T, = desorption temperature, C.
u = superfical linear velocity of gaseous flow cm/sec.
X = dlmenslonless adsorbate concentration in gas phase,
Cf
X* = dlmensionless adsorbate equilibrium concentration in gas phase, —
Cf
Y = dimensionless adsorbate concentration in solid phase, ^~-
\
z = axial distance from top of bed, cm.
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85
GREEK LETTERS
a = ratio of adsorbate removal capacity in the gas phase to that in
in the solid phase in the bed, 7^
H q
s m
3 = residual pollutant loading at the end of desorption
A = dlmensionless axial distance, Z
3
p - density of gas, g/cm .
o
3
p = density of adsorbent g/cm .
T = dimensionless time, tG
L H
g
= void fraction of the bed.
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86
LITERATURE CTTED
Ames, W. F., "Numerical Methods for Partial Differential Equations",
Barnes & Noble, Inc., New York, 1969.
Brunauer, S., "The Adsorption of Gases and Vapors. Volume I, Physical
Adsorption", Princeton University Press, Princeton, N.J., 1943.
Chen, H. T., Hill, F. B., Seperatlon Sci., 6_, All (1971)
Chen, H. T., Rak, J. L., Stokes, J. D., Hill, F. B., AIChE J., 18, 356
(1972).
Danielson, J. A., (editor), "Air Pollution Engineering Manual", U.S. Depart-
ment of HEW, National Center for Air Pollution Control, Cincinnati,
Ohio, 1967.
Fan, L. T., Choi, S. K., Institute for Systems Design and Optimization
Report No. 41, Kansas State University, Manhattan, Kansas.
Faulkner, W. D., Schuliger, W. G., Urbanic, J. E., presented at 74th AIChE
National Meeting, New Orleans, Louisiana, March 12, 1973.
Gregory, R. A., Sweed, H. H., Chem. Eng. Journal, 1., 207 (1970).
Gregory, R. A. Sweed, N. H. ibid, A_, 139 (1972).
Gupta, R., Sweed, N. H., presented at AIChE National Meeting, Minneapolis,
Minnesota, August 29, 1972.
Hassler, J. W., "Activated Carbon", Leonard Hill Books, 1967.
Kowler, D. E., Kadlec, R. H., AIChE J. 18, 1207 (1972).
Levenspiel, 0., "Chemical Reaction Engineering", p. 275, John Wiley &
Sons, New York, 1962.
Mattia, M. M., CEP, 66, 74 (December, 1970).
Pigford, R. L., Baker, B. Ill, Blum, E. E., I&EC Fundamentals, 8_, 144
(1969).
Stern, A. C. (editor), "Air Pollution", Vol. III. Academic Press, 1968.
Sweed, N. H., Wilhelm, R. H., I&EC Fundamentals, J3, 221 (1969).
Treybal, R. E., "Mass-Transfer Operation", 2nd edition McGraw-Hill Book
Company, Inc., New York, 1968.
Wilhelm, R. H., Rice, A. W., Bendelius, A. R., I&EC Fundamentals, 5_, 141
(1966).
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87
Wilhelm, R. H., Rice, A. W., Rolke, R. W., Sweed, N. H., I&EC Fundamentals,
1, 337 (1968).
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89
5. CONCLUSIONS AND RECOMMENDATIONS
The literature survey and mathematical modeling presented in this
report should serve as a convenient reference source for those who are
engaged in analysis, design and operation of gas adsorbers for air
pollutants.
A computer simulation of the processes taking place in an
adsorption bed was carried out, and the combined effect of dispersion and
heat of adsorption on the operating characteristics of the adsorption unit
was determined. Results of this phase of the study should be useful for
advancing the understanding of the behavior of the adsorption unit, for
planning laboratory and field experiments, and for interpreting the results
of such experiments.
Two new operational schemes for a single column adsorber system were
proposed. The performance of such a system was studied by computer simu-
lation. The results of this phase of the study should be useful for design
and operation of such an adsorber system. A single adsorber system can be
installed easily and operated effectively. Such a system should be
especially effective when the limitation of space or weight must be taken
into consideration.
Considerable technical information on air pollutant adsorption and
several valid mathematical models for packed bed adsorbers for air
pollutants are available. While the present study has contributed signi-
ficantly toward practical applications of such information and mathematical
models, much remains to be done. For example, optimization and synthesis
studies should be carried out for multiple bed adsorption systems. For
this purpose improved mathematical models for regeneration should be
developed.
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TECHNICAL REPORT DATA
{Please read Instructions on the reverse before completing)
1 REPORT NO.
EPA-650/2-74-110
3 RECIPIENT'S ACCESSION-NO
4 TITLE AND SUBTITLE
Mathematical Simulation of an Adsorber for
Pollutant Removal
5. REPORT DATE
October 1974
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
L.T. Fan
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING OR6ANIZATION NAME AND ADDRESS
Kansas State University
Manhattan, Kansas 66506
10 PROGRAM ELEMENT NO
1AB015; ROAP 21AXM-061a
11. CONTRACT/GRANT NO
R-800316
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
NERC-RTP, Control Systems Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
13. TYPE OF REPORT AND I
Final; 6/72-12/73
14 SPONSORING AGENCY CODE
16. SUPPLEMENTARY NOTES
16. ABSTRACT Tne first portion of the report: comprehensively surveys the literature on
design and operational aspects of processes for adsorbing gaseous pollutants; and
summarizes mathematical models of these processes. The second portion of the
report: presents mathematical models (based on the mechanism of external mass
transfer rate control and a Langmuir type isotherm) for the adiabatic adsorption
processes in a fixed bed of adsorbent, taking into account axial dispersion of the
pollutant; presents the transient solution (obtained by solving numerically the gover-
ning equations using the Crank-Nicolson implicit method) for the dynamic adsorbate
concentrations and temperature at various bed positions; and presents results of
studies on the effects of various parameters. The third portion of the report:
describes a single fixed-bed pollutant adsorber operated cyclically by synchronizing
the change in direction of the gaseous flow with the change in temperature; presents
two operational schemes for such a system; and discusses effects of several para-
meters on adsorber performance.
17
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Air Pollution
Adsorption
Mathematical Models
Adiabatic Conditions
Air Pollution Control
Stationary Sources
Gaseous Pollutants
13B
12A
20M
18. DISTRIBUTION STATEMENT
Unlimited
19 SECURITY CLASS (ThisReport)
Unclassified
21 NO OF I
90
20.SECURITY CLASS (Thispane)
Unclassified
22 PRICE
EPA Form 2220-1 (9-73)
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